The control of the diffusion coefficient by the dimensionality d of the structure appears as a most promising lever to efficiently tune the release rate from lyotropic liquid crystalline (LLC) phases and dispersed particles towards sustained, controlled and targeted release. By using phosphatidylcholine (PC)- and monolinoleine (MLO)-based mesophases with various apolar structural modifiers and water-soluble drugs, we present a comprehensive study of the dimensional structural control of hydrophilic drug release, including 3-d bicontinuous cubic, 2-d lamellar, 1-d hexagonal and 0-d micellar cubic phases in excess water. We investigate how the surfactant, the oil properties and the drug hydrophilicity mitigate or even cancel the effect of structure variation on the drug release rate. Unexpectedly, the observed behavior cannot be fully explained by the thermodynamic partition of the drug into the lipid matrix, which points out to previously overlooked kinetic effects. We therefore interpret our results by discussing the mechanism of structural control of the diffusion rate in terms of drug permeation through the lipid membrane, which includes exchange kinetics. A wide range of implications follow regarding formulation and future developments, both for dispersed LLC delivery systems and topical applications in bulk phase.